C10 equilibrium
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1. The document discusses concepts related to equilibrium, rotational kinetic energy, angular momentum, and the requirements for an object to be in static equilibrium. 2. It provides examples of situations involving levers, beams, blocks, and ropes and asks questions about the forces and tensions in each case for the object to be in equilibrium. 3. The document also covers topics like center of gravity, elasticity, stress and strain, and defines moduli like Young's modulus, shear modulus, and bulk modulus.
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This document contains chapter 5 from the textbook "Mechanics of Materials" which discusses the analysis and design of beams for bending. It includes introductions to shear and bending moment diagrams, sample problems calculating reactions and drawing the diagrams, relationships between load, shear and bending moment, and considerations for designing prismatic beams for bending. The key concepts covered are determining internal shear forces and bending moments, using equilibrium to draw shear and bending moment diagrams, and selecting beam cross sections based on required section modulus and allowable stresses.
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This document describes the design and construction of a hydraulic pipe bending machine. The machine aims to address common problems with manually operated pipe bending systems, which require tremendous human effort, have high labor costs, and can result in defects. The hydraulic pipe bending machine uses a hydraulic jack to generate large bending forces with minimal human effort. It consists of a base frame, mounting points for pulleys of various diameters, a hydraulic jack between the pulleys, and retraction springs. Pipes are inserted between the pulleys and bent into the desired shape when the hydraulic jack handle is operated. The machine allows for safe and damage-free bending of pipes for applications in automotive, agriculture, and other industries.
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This chapter discusses pure bending of structural members. Pure bending occurs when equal and opposite couples or bending moments act on a member. The chapter covers bending deformations and strains, stress due to bending calculated using elastic flexure formulas, section properties that influence bending such as moment of inertia, and bending of composite members made of multiple materials. Examples are provided to demonstrate calculating bending stresses in reinforced concrete beams.
Theory of bending
This document provides information on bending theory and design principles for bending operations. It discusses the following key points in 3 sentences:
Types of bending covered include V-bending, edge bending, and flanging. Springback occurs as the bent part partially recovers its original shape after bending forces are removed. The document outlines methods to compensate for springback like overbending and bottoming, and provides formulas to estimate springback and calculate bending allowance and force.
Bending
1. The document discusses sheet metal forming processes including shearing, bending, and springback. It provides definitions and formulas for calculating forces in shearing and springback in bending.
2. An lab experiment is described that involves bending aluminum strips using a finger brake machine and measuring the resulting bend radii and angles to analyze springback.
3. Finite element analysis simulations are shown illustrating the deformation during bending and springback.
Design and fabrication of bending machine
This document describes the design and fabrication of a portable bending machine. The machine uses a motor attached to a circular plate to rotate two jigs holding a metal rod, bending it into various shapes. It can bend tubes, bars, channels, and squares into curves or other forms. Calculations are provided for bending stresses and required motor torque. The machine is low-cost and easy to operate, making it suitable for portable use in bending metal.
PROJECT Presentation(2014-15)new
This document describes the design of a hydraulic bending machine. It contains sections on the hydraulic principles, types of bending, hydraulic bending process, components of the machine including the hydraulic jack, roller guides, die and frame. The document explains how the machine works by using a hydraulic jack to apply pressure through a piston rod to rollers, bending a steel bar placed between the rollers and die. It lists advantages like efficiency and safety, and disadvantages like limited thickness bending. Applications include construction and manufacturing. The future scope is to increase capacity and automate the machine.
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Design and fabrication of hydraulic pipe bending machine
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【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
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C10 equilibrium
- 1. 1 Class 24 Review Equilibrium Requirements of Equilibrium Review Rotational Kinetic Energy An object that rotates while its center of mass translates will have both translational and rotational kinetic energies. Kinetic energy of pure rotation Work done by constant torque Power (constant torque) Angular Momentum if Conservation of angular momentum The total angular momentum of a rotating object remains constant if the net external torque acting on it is zero. The net torque acting on an object is equal to the time rate of change of the angular momentum x
- 2. 2 An object with forces acting on it, but not moving, is said to be in static equilibrium. The first condition for equilibrium is that the forces along each coordinate axis add to zero. The second condition of equilibrium is that there be no torque around any axis; the choice of axis is arbitrary. Requirements of Equilibrium For static equilibrium the total momentum must be zero. (P is constant) (L is constant) CT_E1: Which disks are in equilibrium? CT_E2: If the magnitude of the forces are adjusted properly (but not zero), in which situation can the rod be in equilibrium? The lever and mechanical advantage Rr FPF CT_E3: In the figure shown, how large should Fp be to lift the bolder?
- 3. 3 Ex: A diver of weight 580 N stands at the end of a diving board of length L = 4.5 m and negligible mass. The board is fixed to two pedestals separated by a distance d = 1.5 m. Of the forces acting on the board, what is (a) the magnitude of the force from the left pedestal and (b) the magnitude of the force from the right pedestal? y x CT_E4: A diver of weight mg stands at the end of a diving board of length L and negligible mass.
- 4. 4 Ex: Suppose the length of a uniform bar is L = 3.00 m and its weight is 200 N. The block weights 300 N and q = 30.0o. The wire can withstand a maximum tension of T = 500N. (b) If the block is placed at the maximum x, what are the horizontal and vertical components of the force on the bar from the hinge at A? y x (a) What is the maximum possible distance x before the wire breaks. CT_E5: (a) In which case it the force on the rod from the cord the least?
- 5. 5 Ex: A uniform beam of weight 500 N and length L = 3.0 m is suspended horizontally. The least tension that will snap the cable is 1200 N. What value of D corresponds to that tension. y x L D CT_E6: In which case is the tension in the wire the least?
- 6. 6 Ex: A uniform beam, of length L. and mass m = 1.8 kg, is at rest on two scales. A uniform block, with mass M = 2.7 kg, is at rest on the beam, with its center a distance L/4 from the beam’s left end. What do the scales read? y x Center of Gravity The gravitational force mg on a body effectively acts at a single point, called the center of gravity of the body. If g is the same for all parts of a body, then the body’s center of gravity is coincident with the body’s center of mass. CT_E8: Consider the two configurations of books shown below. CT_E9: A box, with its center-of-mass.... CT_E7: You are standing on two bathroom scales, one foot on each. Note: if M was at L/2 each scale would read the same. CT_E10: The figure show a block suspended by two wires, A and B, ...
- 7. 7 Ex: A ladder of length L = 12 m and mass m = 45 kg leans against a frictionless wall. It rests on a floor with coefficient of friction m = 0.5. What is the minimum angle you can lean the ladder so that it does not slip? y x
- 8. 8 x y m Ex: A block of mass 15.0 kg hangs by a cord which is attached to two other cords which hang from the ceiling, as shown. The cords have negligible mass, q1 = 25o and q2 = 40o. What is the tension in the three cords? cord 1 cord 3 cord 2 For m For the knot
- 9. 9 Ex: What magnitude for force applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h = 3.00 cm. r = 6.00 cm and m = 0.800 kg.
- 10. 10 Requirements of Equilibrium Review (P is constant) (L is constant) Class 25 Review Center of Gravity Elasticity
- 11. 11 Elasticity Tension and compression Stress a Strain E - Young’s Modulus (units: N/m2) Atoms in a solid form a lattice structure The atoms are bonded together with electrons. These bond act like springs. There are three ways we can stress solids. We can pull/push, shear, or compress. In all cases CT_E10: The figure show a block suspended by two wires, A and B, which are identical except for their original lengths.
- 12. 12 Shearing Hydraulic Stress G - Shear Modulus (units: N/m2) b - Bulk Modulus (units: N/m2)